Pickslides, the fact that the problem mentions a "general" solution should tell you that this problem does NOT have one unique solution and so the matrix A is NOT invertible!

|flipboi| you did not write the original equations as a matrix and I see no reason to do so. You are making this much more difficult that it should be.

x+y+z = 0
2x+2y+2z = 0
3x+3y+3z= 0

are all the same equation! So you really just have z= -x- y. That is the "general solution". x and y can be any numbers at all and z= -x- y.

If you really intended then the vector solution is

Row reducing to
just tells you, again, that all three equations reduce to x+ y+ z= 0 so that z= -x -y.

"but i don't get how y=s and z= t". I solved for z= -x- y so I could use x and y as parameters or just rename them "s" and "t" and write the solution as x= s, y= t, z= -s- t. Apparently in your text, they solve for x= -y- z. You don't "get" y= s and z= t, you assign those names. Just rename "y" as "s" and "z" as "t". Then x= -s- t, y= s, z= t. There are an infinite number of ways to write parametric equations for a "general" solution.